Seismograms are commonly transformed into tau-p space to facilitate processing, filtering, deconvolution, and the like. The inversion method used to calculate the transformated data becomes unstable at low frequencies. The artifacts from this instability lead to undesired effects after tau-p domain processing and transformation back to the time-distance domain. Furthermore, current implementations of the transformation lead to a transform domain which is artificially poor in sampling in the low frequencies.
A previous solution has been to attempt to stabilize the inversion by the use of a standard, frequency independent noise factor. However, such a noise factor does not attack the problem with sufficient specificity, and the instability remains. The spectral imbalance of the transform domain has simply been tolerated, even though it has deleterious effects on some transform domain processes such as deconvolution. Therefore, a heretofore unaddressed need exists in the industry to address the aforementioned deficiencies and inadequacies.